Department of Mathematical Sciences, Unit Catalogue 2008/09 |
MA20201 Modelling the dynamics of life 1 |
| Credits: 6 |
| Level: Intermediate |
| Semester: 1 |
| Assessment: EX75CW25 |
| Requisites: |
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Aims: To provide students with the necessary mathematical background to be able to model processes in the life sciences.
Learning Outcomes: At the end of this unit, students should be able to: * manipulate and make effective use of a range of standard mathematical functions; * integrate and differentiate a range of standard mathematical functions; * write down and analyse a range of simple mathematical models and interpret the results biologically. Skills: Calculus (T, A); modelling (T, F, A). Content: Exponentials, logarithms and trigonometric functions. First-order linear difference equations: solutions, steady states, stability; biological applications, e.g. bacterial population growth, gas exchange in the lung. Limits and derivatives: differentiation of standard functions; product rule, quotient rule, chain rule. Applications of derivatives, e.g. maximum sustainable yield, optimal foraging, maximising oxygen uptake. First-order ordinary differential equations; solution by separation of variables, integrating factor; applications, e.g. rate equations, exponential growth, Bertanffy growth. |